THANKS!! In a rocket - propulsion problem the mass is variable. Another such pro

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THANKS!!

In a rocket - propulsion problem the mass is variable. Another such problem is a raindrop falling through a cloud of small water droplets. Some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. The force on the raindrop is Fext = dp/dt = m dv/dt + v dm/dt Suppose the mass of the raindrop depends on the distance x that it has fallen. Then m = kx, where k is a constant, and dm/dt = kv. This gives, since Fext, = mg, mg = m dv/dt + v (kv) Or, dividing by k, xg = x dv/dt + v2 This is a differential equation that has a solution of the form v = at, where a is the acceleration and is constant. Take the initial velocity of the raindrop to be zero. Using the proposed solution for v, find the acceleration a. Find the distance the raindrop has fallen in t = 3.50 s. Given that k = 2.00 g.m, find the mass of the raindrop at t = 3.50 s.

Explanation / Answer

Online homework can be frustrating because it never specifies how to correctly input the answer. You are doing the problem correctly. a = g/2 x = (g*t^2)/4 m = kx = (2g/m)*x The following link may help you: http://books.google.com/books?id=5Bql9o21yv0C&pg=PA237&lpg=PA237&dq=raindrop+falling+through+a+cloud+of+small+water+droplets&source=bl&ots=sNgfRJw0gc&sig=z_Wea2mscwBHp_OUs_lqtKmSj4A&hl=en&ei=23u_TsbGH6LjmAWmp-CiBA&sa=X&oi=book_result&ct=result&resnum=5&ved=0CEEQ6AEwBA#v=onepage&q=raindrop%20falling%20through%20a%20cloud%20of%20small%20water%20droplets&f=false **your question is on page 237 and the answers are explains on page 238. It doesn't look like you are having any trouble, but there are other answers too in case you are having similar problems.

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